For alto, there are two major ways of playing it. Grumps is right, figure out f# first as it really helps.
The old school cats like Bird and Stitt used to play it with 1+3 (B, G) in the left hand, and f (1) and side Bb. With this wacky method, g# is played by moving from side Bb to side C. It gets the notes out but it's pretty dicey in fast passages etc., which is why those guys never really approached the high G from a half step or whole step.
I learned this next one watching Dave Binney play.
If F# is lhs Fork key, lhs C, side Bb on the rhs - you lift up the lhs C and slam down the rhs f. For g# you then just lift up the rhs f so that it's just the lhs fork key and side Bb. From then on up, you use your left hand a and c for a, and then 6ths to D, and 8ths above that. Overtones and long tones make this stuff possible. Without the work, you will be searching for a different mouthpiece and will never get the right sound. Good luck!!!